What does a compound inequality express?

A compound inequality expresses two inequalities combined into one statement. This involves the use of logical connectors such as "and" or "or" to link the inequalities. For example, in a compound inequality like (x > 3) and (x < 7), both conditions must hold true simultaneously for the values of (x) to satisfy the inequality. This structure allows for a more comprehensive way to represent a range of values rather than just a single constraint.

The ability to combine multiple inequalities is essential in various applications, such as finding acceptable values in real-world contexts (e.g., determining a temperature range or speed limits), and is a fundamental concept in algebra that students encounter regularly. Understanding compound inequalities helps in graphing, interpreting solutions, and solving complex problems that involve multiple conditions.